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Calculus III (Practice Problems) / Surface Integrals / Surface Integrals of Vector Fields   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Practice Problems
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Surface Integrals Previous Section   Next Section Stokes' Theorem

 

1. Evaluate  where  and S is the portion of  that lies over the triangle in the xy-plane with vertices ,  and  oriented in the negative z-axis direction.  [Solution]

 

2. Evaluate  where  and S is the portion of  that lies behind  oriented in the positive y-axis direction. [Solution]

 

3. Evaluate  where  and S is the portion of  between  and  oriented outwards (i.e. away from the x-axis).  [Solution]

 

4. Evaluate  where  and S is the portion of the sphere of radius 3 with ,  and  oriented inward (i.e. towards the origin). [Solution]

 

5. Evaluate  where  and S is the surface of the solid bounded by , ,  and  with the positive orientation.  Note that all four surfaces of this solid are included in S. [Solution]

 

6. Evaluate  where  and S is the surface of the solid bounded by , , and  with the negative orientation.  Note that all three surfaces of this solid are included in S. [Solution]

 

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Surface Integrals Previous Section   Next Section Stokes' Theorem
Line Integrals Previous Chapter  

Calculus III (Practice Problems) / Surface Integrals / Surface Integrals of Vector Fields    [Notes] [Practice Problems] [Assignment Problems]

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